This gets the full command from PID 1 and checks for the process running

healthcheck.sh

#!/bin/sh
set -e

# Get the process
FULL_COMMAND="$(sed -n l "/proc/1/cmdline" | sed -e 's/\\$//g' | tr -d '\n' | sed -e 's/\$$//g' | sed -e 's/\\000/ /g' | sed -e 's/ *$//g' | head -1)"

# Look for the process
pgrep --full "$FULL_COMMAND" 2> /dev/null > /dev/null;
exit ${?};

This is "a way" to put in a generalized HEALTHCHECK within a Dockerfile:

COPY healthcheck.sh /app/healthcheck.sh
RUN chmod a+x /app/healthcheck.sh

USER nobody
HEALTHCHECK --interval=30s --timeout=30s --start-period=5s --retries=3 CMD [ "/app/healthcheck.sh" ]
ENTRYPOINT ["executable", "to", "run"]